For the numerical simulations of section , we use the formulation introduced in [1]}, which readily adapts to the viscoelastic setting. The formulation is based on a combination of works by Moreau, et al. [2]} and Maxian, et al. [3]}. For convenience, we recall the original formulation (REF )-(REF ) of the viscoelastic resistive force theory equations:
\(\begin{aligned}\frac{\partial \mathbf {X}}{\partial t}(s,t) &= -(1+\mu )\big ({\bf I}+\gamma \mathbf {X}_s\mathbf {X}_s^{\rm T}\big )\big (\mathbf {X}_{sss}-\tau \mathbf {X}_s-(\kappa _0)_s\mathbf {e}_{\rm n}-\frac{\mu }{1+\mu }\xi _s\mathbf {e}_{\rm n}\big )_s \\\delta \dot{\xi }&= -\xi + \kappa - \kappa _0 \\\left|\mathbf {X}_s \right|^2&=1 \\(\mathbf {X}_{ss}-\kappa _0\mathbf {e}_{\rm n})\big |_{s=0,1}&=0\,, \quad (\mathbf {X}_{sss}-\tau \mathbf {X}_s-(\kappa _0)_s\mathbf {e}_{\rm n})\big |_{s=0,1}=0\,, \quad \xi \big |_{s=0,1}=\xi _s\big |_{s=0,1}=0\,.\end{aligned}\) 
